Luz was born in Cambridge, Massachusetts. He performed in various stage productions during the 1970s, and made his film acting debut in the 1979 drama Voices, which also marked the film debut of fellow TNG guest star Thelma Lee. After completing work on this film, Luz made his Broadway debut in the 1979 revival of the musical play Whoopee! Luz then won the role of Dr. John Bennett on NBC's daytime drama series The Doctors. He starred in this series for two seasons, from 1979 through 1981, and received a nomination from the Daytime Emmy Awards as Outstanding Actor in a Daytime Drama Series for his performance.

After leaving The Doctors, Luz returned to performing in theater. He starred as crazed and abusive dentist Orin Scrivello in an early 1980s production of the musical Little Shop of Horrors, for which he was nominated for a 1983 Drama Desk Award as Outstanding Featured Actor in a Musical. He returned to film in 1984, co-starring with TOS guest actress Julie Newmar in the independent drama Love Scenes. He also returned to television, making guest-appearances on two hit NBC series: the Robert Butler-created Remington Steele and action drama The A-Team, starring Dwight Schultz.

In 1985 and 1986, Luz starred in two short-lived CBS series, Hometown and Kay O'Brien; the latter series co-starred Keone Young. Also in 1986, Luz appeared in the CBS TV movie Classified Love, along with Michael McKean. Luz followed these projects with guest spots on NBC's Hunter (with Bruce Davison and Leslie Hope) and The Facts of Life. He also co-starred with Robert Lansing in the horror film The Nest and starred opposite Jimmie F. Skaggs in the horror western Ghost Town, both released in 1988. The following year, Luz made guest appearances on such shows as Beauty and the Beast (starring Ron Perlman) and had a supporting role in the hit comedy film When Harry Met Sally...

In 1991, following his appearance on TNG, Luz had a recurring role on the NBC series Sisters. He then guest-starred in two episodes of Matlock – one with Robin Christopher and another directed by Leo Penn and co-starring Nick Tate. He has since guest-starred on such television shows as Walker, Texas Ranger (starring Noble Willingham), JAG (with Kevin Conway and David Sage), and Baywatch. He was also briefly a regular on the ABC soap opera All My Children in 1993.

Luz can also be seen in the 1995 film Don Juan DeMarco, along with Tommy "Tiny" Lister, Jr.. His most recent films were The Pornographer, starring Craig Wasson, and Restraining Order, co-starring Dean Stockwell. Both of these films were released in 1999. After the latter project, Luz retired from acting and became involved in many New York area museums and exhibition halls as a trustee and a tour guide.